Unit 7: Waves

• Progressive wave:

  • Transfers energy from one place to another in a wave front
  • Travels through material
  • Contrasts with stationary waves that don't provide a net transfer of energy
• Longitudinal wave:

  • Particles oscillate in the same direction as the energy propagation
  • Comprises rarefactions (areas of low pressure) and compressions (areas of high pressure)
• Transverse wave:

  • Particle oscillations are oriented perpendicularly to the direction of energy propagation
  • Example: electromagnetic waves
• Motion of a rope when moved up and down while the other end is held still:

  • Forms a vertically oscillating wave that travels towards the partner and decreases in amplitude
  • Classified as a transverse progressive wave
• Motion of a spring when a mass is suddenly hung from the end:

  • Spring oscillates up and down around a central position of equilibrium
  • Eventually comes to rest at the equilibrium point
  • Wave produced is longitudinal and standing
• Motion of water particles in a ripple tank:

  • Particles oscillate up and down while the wave travels linearly across the water surface
  • Wave produced is progressive and transverse
• Frequency:

  • Number of waves passing through a point per second
  • Units: Hertz (Hz) or s^-1
• Wavelength:

  • Distance between two adjacent corresponding points (e.g., peaks) on a wave
• Amplitude:

  • Maximum displacement of the wave from its equilibrium position
• Calculating time period of a wave using frequency:

  • T = 1/f
• Determining velocity of a progressive wave from frequency and wavelength:

  • Velocity (v) = frequency (f) x wavelength (λ)
• Phase difference of a wave:

  • Amount one wave lags behind another as a proportion of the wavelength
  • Measured in radians or degrees
• Axes on an oscilloscope:

  • Vertical divisions measure voltage/amplitude of the wave
  • Horizontal divisions measure time (used to find time period and frequency)
• 1. gain and time-base setting on the oscilloscope:

  • Y-gain determines volts 'per division' on the vertical scale (amplitude)
  • Time-base setting dictates time 'per division' on the horizontal scale
• Intensity defined in terms of power:

  • Intensity = power / area
• Intensity and amplitude relationship:

  • Intensity is proportional to amplitude squared (Intensity ∝ Amplitude^2)
• Determining frequency of sound with a CRO:

  • Find time period of the wave using the CRO
  • Count squares for one wave period and multiply by the time for each square
  • Use f = 1/T to find the inverse and determine the frequency of the wave
• 
  

  The wavelength of sound using a stationary wave is calculated by finding the distance D between the nodes and antinodes and then using: D = 0.5 x wavelength
• The Doppler effect is an observed change in the frequency of any wave caused by the movement of the wave source relative to the observer
• In the Doppler effect, when the source moves towards the observer, each vibration reaches the observer in a time less than the previous vibration
• The frequency change in the Doppler effect is dependent on the velocity of the source relative to the observer
• Electromagnetic waves all travel at the same speed, but their wavelengths, frequencies, and hence periods vary.
• The magnetic field and electric field in an electromagnetic wave are not parallel to each other, they are perpendicular.
• The order from highest to lowest frequency for X-rays, UV, Visible, Microwaves, Radio is: X-rays, UV, Visible, Microwaves, Radio
• The highest frequency form of electromagnetic radiation is Gamma radiation with a frequency greater than 10^19 Hz
• Infrared radiation has a wavelength of approximately 1 μm, ranging between ~700nm and 1mm
• Visible light has a range of wavelengths between 400-700 nm
• Microwaves can be polarised using a metal grid instead of a polarising filter
• Polarisation is the process of blocking all but one plane of vibration of a transverse wave
• Polarised waves only contain waves oscillating along one axis, while unpolarised waves can oscillate in any direction perpendicular to the axis of propagation
• Longitudinal waves cannot be polarised because particles in a longitudinal wave oscillate parallel to the direction of propagation
• When polarised light is passed through a rotating polarisation filter, the intensity of the light passing through varies from a maximum to a minimum based on the alignment of the axes of polarisation and the filter
• Doppler Effect

  A) observed frequency

  B) actual frequency

  C) velocity of sound waves

  D) velocity of observer

  E) velocity of source

  
• If an object emitting sound moves away from us, we hear a lower pitch than when it was stationary (red shift)
• If an object emitting sound moves towards us, we hear a higher pitch than when it was stationary (blue shift)
• The intensity of a transverse wave passing through a polarising filter either reduces or remains unchanged, defined by Malus’s law:

  $I=$$I_{0}\times \cos ^{2}\Theta$
• Malus's Law states that the intensity of a transverse wave passing through a polarising filter either reduces or remains unchanged depending on the angle between the axis of polarisation and the plane containing the incident ray and the normal to the surface of the filter.